Bayes’ Theorem is a mathematical concept used in probability theory that enables us to update our beliefs or predictions about a particular event or situation based on new information or evidence. It helps us to calculate the probability of an event occurring given some prior knowledge and new evidence. In other words, it allows us to revise our initial beliefs or assumptions based on new data that we gather.
The theorem is based on conditional probabilities, which means that it involves calculating the likelihood of an event occurring given some other event. Bayes’ Theorem can be expressed mathematically as P(A|B) = P(B|A) * P(A) / P(B), where P(A) is the prior probability of event A, P(B) is the prior probability of event B, P(B|A) is the conditional probability of event B given event A, and P(A|B) is the probability of event A given event B. Bayes’ Theorem has a wide range of applications, including in medicine, engineering, and finance, and it is a fundamental concept in machine learning and artificial intelligence